unit iii: objectives3.pdf1. a poorly tuned yugo can accelerate from rest to a speed of 28 m/s in 20...

UNIT III: Objectives What you should know when all is said and done

1. You should be able to determine the instantaneous velocity of an object in three ways:

a. determining the slope of the tangent to an x vs t graph at a given point. b. using the mathematical model v f = at + vi c. using the mathematical model v f

2 = vi2 + 2ax

2. You should be able to determine the displacement of an object in three ways:

a. finding the area under a v vs t curve b. using the mathematical model x = 12 at

2 + vit c. using the mathematical model v f

2 = vi2 + 2ax

3. You should be able to determine the acceleration of an object in five ways:

a. finding the slope of a v vs t graph b. using the mathematical model a =

ΔvΔt

c. rearranging the mathematical model x = 12 at2 + vit

d. rearranging the mathematical model v f = at + vi e. rearranging the mathematical model v f

2 = vi2 + 2ax

4. Given a x vs t graph, you should be able to:

a. describe the motion of the object (starting position, direction of motion, velocity) b. draw the corresponding v vs t graph c. draw the corresponding a vs t graph d. draw a motion map for the object (including v and a vectors) e. determine the instantaneous velocity of the object at a given time

5. Given a v vs t graph, you should be able to: a. describe the motion of the object (direction of motion, acceleration) b. draw the corresponding x vs t graph c. draw the corresponding a vs t graph d. draw a motion map for the object (including v and a vectors) e. write a mathematical model to describe the motion

f. determine the acceleration g. determine the displacement for a given time interval Additionl Study Hints: Look over all the old worksheets and quizzes. Make up a x vs t graph and see if you can draw the v vs t and a vs t graphs. Get together with your lab partners and review.

Name

Date Pd

UNIT III: Worksheet 1 When evaluating problems 1 - 3, please represent the motion that would result from the rail

configuration indicated by means of a: A) qualitative graphical representation of x vs. t B) qualitative graphical representation of v vs. t C) qualitative graphical representation of a vs. t D) qualitative motion map

E) general mathematical expression of the relationship between x and t

F) general mathematical expression of the relationship between v and t

G) general mathematical expression of the relationship between a and t

1)

D) x E) _____________________________ F) ____________________________ G)____________________________

t

t

v

t

a

x

©Modeling Workshop Project 2002 3 Unit III Objectives v2.0

2)

D) x E) _____________________________ F) ____________________________ G)____________________________

t

t

v

t

a

x


3)

D) x E) _____________________________ F) ____________________________ G)____________________________

t

t

v

t

a

x


When considering problems 4-5, assume that the ball does not experience any change in velocity while it is on a horizontal portion of the rail.

Please represent the motion that would result from the rail configuration indicated by means of a:

A) qualitative graphical representation of x vs. t B) qualitative graphical representation of v vs. t C) qualitative graphical representation of a vs. t D) qualitative motion map

4)

D) x

t

t

v

t

a

x


5)

D) x

t

t

v

t

a

x


Unit III: Stacks of kinematics curves Given the following position vs time graphs, sketch the corresponding velocity vs time and

acceleration vs time graphs.


For the following velocity vs time graphs, draw the corresponding position vs time and acceleration vs time graphs.


Name

Date Pd

UNIT III: Worksheet 2 While cruising along a dark stretch of highway with the cruise control set at 25 m/s (≈55 mph), you see, at the fringes of your headlights, that a bridge has been washed out. You apply the brakes and come to a stop in 4.0s. Assume the clock starts the instant you hit the brakes.

1. Construct a motion map that represents the motion described above, including position, velocity,

and acceleration. Clearly demonstrate how you can determine the direction (sign) of the acceleration from the motion map representation.

2. Construct qualitative graphical representations of the situation described above to illustrate:

a. x vs. t b. v vs. t c. a vs. t


3. Construct a quantitatively accurate v vs t graph to

describe the situation. 4. On the v vs t graph at right, graphically represent

the car’s displacement during braking. 5. Utilizing the graphical representation, determine

how far the car traveled during braking. (Please explain your problem solving method.)

6. In order to draw the a vs t graph, you need to

determine the car’s acceleration. Please do this, then sketch a quantitatively accurate a vs t graph

7. Using the equation you developed for displacement of an accelerating object determine how far

the car traveled during braking. (Please show your work.) 8. Compare your answers to 5 and 7.


Name

Date Pd

UNIT III: Worksheet 2a

This time, while cruising along a dark stretch of highway at 30 m/s (≈65 mph), you see, at the fringes of your headlights, some roadkill on the highway. It takes you 0.5 s to react, then you apply the brakes and come to a stop 3.5s later. Assume the clock starts the instant you see the hazard.

1. Construct a motion map that represents the motion described above, including position, velocity,

and acceleration. Hint: make the dots at 0.5s intervals.

2. Construct a quantitatively accurate v vs t graph to

describe the situation. 3. On the v vs t graph at right, graphically represent

the car’s displacement during this incident. 4. Utilizing the graphical representation, determine

how far the car traveled during this incident. (Please explain your problem solving method.)

5. In order to draw the a vs t graph, you need to

determine the car’s acceleration once the brakes were applied. Please do this, then sketch a quantitatively accurate a vs t graph


6. Two kinds of motion occur in this case. For the first 0.5s, the car is traveling at constant

velocity. For the remainder of the time, the car has an initial velocity and a uniform acceleration. Using the appropriate mathematical representation for each phase of the motion, determine how

far the car traveled from the instant you noticed the hazard until you came to a stop. As always, show work and include units. 7. Compare your answers to 4 and 6.


Name

Date Pd

UNIT III: Worksheet 3 1.

x (m

)

t (s)0 5

25

a. Describe in words the motion of the object from 0 - 6.0 s. b. Construct a qualitative motion map to describe the motion of the object depicted in the graph

above. c. What is the instantaneous velocity of the object at the following times? i. t = 1.0 s ii. t = 3.0 s d. What is the simple average of these two velocities? What is the average velocity for the entire interval? Why are these two values different? Which is best to describe the motion of the object?


e. Graphically represent the relationship between velocity and time for the object described above.

t (s)0

v (m

/s)

f. From your velocity vs. time graph determine the total displacement of the object.

2. The graph below represents the motion of an object. x

tA

B

D

E

F

G

C

a. At what point(s) on the graph above is the object moving most slowly? (How do you know?) b. Over what intervals on the graph above is the object speeding up? (How do you know?) c. Over what intervals on the graph above is the object slowing down? (How do you know?) d. At what point(s) on the graph above is the object changing direction? (How do you know?)


3. A stunt car driver testing the use of air bags drives a car at a constant speed of 25 m/s for a total of 100. m. He applies his brakes and accelerates uniformly to a stop just as he reaches a wall 50. m away.

a. Sketch qualitative position vs. time and velocity vs time graphs.

b. How long does it take for the car to travel the first 100.m?

c. Remember that the area under a velocity vs time graph equals the displacement of the car. How long must the brakes be applied for the car to come to a stop in 50 m?

d. Now that you know the total time of travel, sketch a quantitative velocity vs time graph.

e. What acceleration is provided by the brakes? How do you know?


Name

Date Pd

UNIT III: Worksheet 4 1. A poorly tuned Yugo can accelerate from rest to a speed of

28 m/s in 20 s. a) What is the average acceleration of the car? b) What distance does it travel in this time?

2. At t = 0 a car has a speed of 30 m/s. At t = 6 s, its speed is

14 m/s. What is its average acceleration during this time interval?

3. A bear spies some honey and takes off from rest, accelerating

at a rate of 2.0 m/s2. If the honey is 16 m away, how fast will his snout be going

at the moment of ecstasy?

4. A bus moving at 20 m/s (t = 0) slows at a rate of 4 m/s each

second. a) How long does it take the bus to stop?

b) How far does it travel while braking?


5. A physics student skis down a hill, accelerating at a constant

2.0 m/s2. If it takes her 15 s to reach the bottom, what is the length of the

slope? 6. A dog runs down his driveway with an initial speed of 5 m/s

for 8 s, then uniformly increases his speed to 10 m/s in 5 s. a) What was his acceleration during the 2nd part of the motion? b) How long is the driveway?

7. A mountain goat starts a rock slide and the rocks crash down

the slope 100 m. If the rocks reach the bottom in 5 s, what is their acceleration? 8. A car whose initial speed is 30 m/s slows uniformly to 10 m/s

in 5 seconds. a) Determine the acceleration of the car. b) Determine the distance it travels in the 3rd second (t = 2s to t = 3s).


UNIT III: Review Use the graph below to answer questions #1-4 that follow:

1. Give a written description to describe the motion of this object. 2. Draw the motion map for the object. Include velocity and acceleration vectors. 3. Explain how you could determine the instantaneous velocity of the object at t = 2 s. 4. Assume the initial velocity was 50 m/s; determine the acceleration of the object. 5. A Pontiac Trans-Am, initially at rest, accelerates at a constant rate of 4.0 m/s2 for 6 s. How fast

will the car be traveling at t = 6 s? 6. A tailback initially running at a velocity of 5.0 m/s becomes very tired and slows down at a

uniform rate of 0.25 m/s2. How fast will he be running after going an additional 10 meters?


7. For each of the position vs time graphs shown below, draw the corresponding v vs t, a vs t , and motion map.

8. Using the graph below, compare the kinematic behavior of the two objects.

Comparison: is A > B, A < B, or A = B, How do you know? a. Displacement at 3 s b. Average velocity from 0 - 3 s c. Instantaneous velocity at 3 s

unit iii: objectives3.pdf1. a poorly tuned yugo can accelerate from rest to a speed of 28 m/s in 20...

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